Seasonal inter-relationships in atmospheric methane and companion δ13C values: effects of sinks and sources

Recent developments in applying carbon-isotope information to better understand regional and global methane budgets infer a strong role by a highly fractionating seasonal sink such as atomic chlorine. Specifically, OH as the predominant seasonal sink cannot account for the 'phase ellipses' based on observed seasonal cycles of methane mixing ratio and isotope ratio, delta C-13. Although a strong role by atomic chlorine is inferred empirically, open questions remain about the interplay between sources and sinks in determining the properties of phase ellipses. This paper employs a simple didactic model of the seasonal cycling of atmospheric methane to understand such interplay. We demonstrate that a single seasonal sink and seasonal source act together to imprint anti-phase seasonalities on atmospheric methane and delta C-13, which lead to phase ellipses that collapse onto a straight line with slope characteristic of that sink. This explains empirical findings of these anti-phase relationships in three-dimensional modelling studies. We also demonstrate that multiple seasonal sinks acting with a seasonal source can yield surprising properties for the phase ellipse that not only explain some features of phase ellipses reported in modelling studies but also have the potential to explain marked inter-annual variation in phase ellipses based on observation.